Question: Simplify; express your answer in exponential form. Assume $p\neq 0, x\neq 0$. $\dfrac{{(p^{3}x)^{2}}}{{(px^{-5})^{-2}}}$
Answer: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(p^{3}x)^{2} = (p^{3})^{2}(x)^{2}}$ On the left, we have ${p^{3}}$ to the exponent ${2}$ . Now ${3 \times 2 = 6}$ , so ${(p^{3})^{2} = p^{6}}$ Apply the ideas above to simplify the equation. $\dfrac{{(p^{3}x)^{2}}}{{(px^{-5})^{-2}}} = \dfrac{{p^{6}x^{2}}}{{p^{-2}x^{10}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{6}x^{2}}}{{p^{-2}x^{10}}} = \dfrac{{p^{6}}}{{p^{-2}}} \cdot \dfrac{{x^{2}}}{{x^{10}}} = p^{{6} - {(-2)}} \cdot x^{{2} - {10}} = p^{8}x^{-8}$